Open AccessAnomalous subdiffusion with multispecies linear reaction dynamics
Author(s) -
T. A. M. Langlands,
B. I. Henry,
Susan L. Wearne
Publication year - 2008
Publication title -
physical review e
Language(s) - English
Resource type - Journals
eISSN - 1550-2376
pISSN - 1539-3755
DOI - 10.1103/physreve.77.021111
Subject(s) - mesoscopic physics , statistical physics , continuous time random walk , reaction–diffusion system , monte carlo method , reaction dynamics , reaction rate , random walk , chemical kinetics , diffusion , dynamics (music) , anomalous diffusion , physics , kinetics , mathematics , thermodynamics , chemistry , classical mechanics , molecule , quantum mechanics , computer science , biochemistry , statistics , acoustics , catalysis , innovation diffusion , knowledge management
We have introduced a set of coupled fractional reaction-diffusion equations to model a multispecies system undergoing anomalous subdiffusion with linear reaction dynamics. The model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics. The effect of reactions is manifest in reaction modified spatiotemporal diffusion operators as well as in additive mean field reaction terms. One consequence of the nonseparability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species. The general solution is derived for the multispecies system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail. We have carried out Monte Carlo simulations corresponding to these special cases and we find excellent agreement with theory
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